{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 588,
   "metadata": {},
   "outputs": [],
   "source": [
    "title = \"Data/ising-exact-occs-N_s16-J0.4-h1-g0.01-width1.5-dt0.1.txt\"\n",
    "exact_data = np.loadtxt(title, dtype='float')\n",
    "title = \"Data/ising-approx-occs-N_s16-J0.4-h1-g0.01-width1.5-dt0.1.txt\"\n",
    "trunc_data = np.loadtxt(title, dtype='float')\n",
    "title = \"Data/ising-approxu-occs-N_s16-J0.4-h1-g0.01-width1.5-dt0.1.txt\"\n",
    "truncu_data = np.loadtxt(title, dtype='float')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 589,
   "metadata": {},
   "outputs": [],
   "source": [
    "J = 0.4\n",
    "h = 1\n",
    "g = 0.01\n",
    "dt = 0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 590,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "121"
      ]
     },
     "execution_count": 590,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(trunc_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 591,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "121"
      ]
     },
     "execution_count": 591,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(exact_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 592,
   "metadata": {},
   "outputs": [],
   "source": [
    "N_s = len(exact_data[0])\n",
    "N_t = len(exact_data)\n",
    "\n",
    "sites = np.linspace(0, N_s-1, N_s)\n",
    "times = np.linspace(0, N_t * dt, N_t)\n",
    "Sites, Times = np.meshgrid(sites, times)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 593,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.QuadMesh at 0x7c5d43244410>"
      ]
     },
     "execution_count": 593,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.pcolormesh(Sites, Times, exact_data, cmap='inferno')\n",
    "# plt.xlabel(r'site $j$')\n",
    "# plt.ylabel(r't')\n",
    "# title = r'$\\langle N_j (t) \\rangle$: $N_s = $' + str(N_s)\n",
    "# title += r', $J = $' + str(J)\n",
    "# title += r', $h = $' + str(h)\n",
    "# title += r', $g = $' + str(g)\n",
    "# title += r', $\\Delta t=$' + str(dt)\n",
    "# plt.title(title)\n",
    "# plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 594,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7c5d43572850>"
      ]
     },
     "execution_count": 594,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.pcolormesh(Sites, Times, truncu_data, cmap='inferno')\n",
    "plt.xlabel(r'site $j$')\n",
    "plt.ylabel(r'time t')\n",
    "title = r'(a) $\\langle N_j (t) \\rangle$'\n",
    "# title += r' $N_s = $' + str(N_s)\n",
    "title += r', $J = $' + str(J)\n",
    "title += r', $h = $' + str(h)\n",
    "title += r', $g = $' + str(g)\n",
    "# title += r', $\\Delta t=$' + str(dt)\n",
    "plt.title(title)\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 578,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '(c) Relative Error $\\\\langle N_j(t) \\\\rangle$, $J = $0.4, $h = $1, $g = $0.01')"
      ]
     },
     "execution_count": 578,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "diffs = np.abs(exact_data - trunc_data) / trunc_data * 100\n",
    "plt.pcolormesh(Sites, Times, diffs, cmap='inferno')\n",
    "plt.colorbar()\n",
    "plt.xlabel(r'site $j$')\n",
    "plt.ylabel(r't')\n",
    "title = r'(c) Relative Error $\\langle N_j(t) \\rangle$' \n",
    "# title += r'$\\langle N_j \\rangle$: $N_s = $' + str(N_s)\n",
    "title += r', $J = $' + str(J)\n",
    "title += r', $h = $' + str(h)\n",
    "title += r', $g = $' + str(g)\n",
    "plt.title(title)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 570,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '(a) MPS Initial State ')"
      ]
     },
     "execution_count": 570,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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AwRQu5NtcXUK54mMvlFVFnkOefj2iciAAweN9deCU2k9cq20HTrm6FMD0uB7hLghA8Gh5+TaNWfadzpy/oDHLv1Me7zwvi3fnFadnz54aPXq0q8uoMFyPcCcEIHi0hVsO6WBGtiTpwMlsLdxyyLUFubmKendusVguOT333HPluv+yuOuuuzRgwIAC8zds2CCLxVKiryNYtmyZJk6caH8cHh6uxMTEshfpprge4U4IQPBYaVnnNWPNPod5L675UWlZ511UkXuryHfnv/zyi31KTExUUFCQw7zHH3/cvqxhGLpw4UK51eJKISEhJf4F6+LIzc11+jbLiusR7oYABI/1/Mo9yss3HObl5ts06ZO9LqrIvVXku/OwsDD7FBwcLIvFYn/8ww8/qFq1avrss88UGRkpPz8/bd68udA7L6NHj1bPnj3tj3v27KlHHnlETz75pEJCQhQWFlbgbtLp06d1//33q06dOvL391erVq20cuVKp7fxueeeU7t27bRo0SKFh4crODhYd9xxh86cOeNQ78WPwHr27KnDhw/rscces98Jk6RTp05pyJAhql+/vgICAtS6dWu98847Dvvq2bOnRo0apdGjR6tmzZqKiYnR3Xffrb/97W8Oy+Xl5al27dp68803nd7ey+F6hLshAMEjbdmfoY93/aJ8m+MLbr7N0Ec7T2jrfjpg/pk7vjv/17/+pSlTpmjv3r1q06ZNsddbuHChAgMDtW3bNk2bNk0TJkzQ2rVrJUk2m0033XSTvvzyS7311lvas2ePpkyZUm7fe7N//359+OGHWrlypVauXKmNGzdqypQphS67bNkyXXHFFZowYYL9TpgknT9/XpGRkfrkk0+0e/du3XfffRo+fLi2b99eoN2+vr768ssvNXv2bN17771atWqVfTuStHLlSp07d06DBw8ul/YWhesR7ogvQkSlNX78+CKf25QbLilUUmFDew2NnbdS3X0PFbl+QkJCGaurXC717vyVIe1dUtOECRPUu3fvEq/Xpk0b+/Fr2rSpXnvtNSUlJal3795at26dtm/frr179+qqq66SJDVq1Mipdf+ZzWbTggUL7B9zDR8+XElJSZo0aVKBZUNCQmS1WlWtWjWFhYXZ59evX9/hI8GHH35Yq1ev1nvvvadOnTrZ5zdt2lTTpk1z2ObVV1+tRYsW6cknn5QkzZ8/X4MGDVLVqlWd2k6J6xGVD3eA4JGaWE+p8BdbSbKoqTWjIstxa+767jwqKqpU6/31blHdunXtP/OQkpKiK664wh5+ylt4eLhDH58/11Jc+fn5mjhxolq3bq2QkBBVrVpVq1ev1pEjRxyWi4yMLLDuvffeq/nz50uS0tLS9Nlnn+nuu+8uRUvKhusR7ogABI9U13pGEV6nZJHjH3WLDEV4nVKY9ayLKnM/y5KPy6uIv01eFmlp8rGKLej/BQYGOtbi5SXDcDyehX1rsY+Pj8Nji8Uim+2PDt0Xf/KhLIKCgpSZmVlg/unTp2W1Wh3qvlQtxTV9+nS9/PLLeuqpp7R+/XqlpKQoJiamQEfnv/57SdKIESN04MABbd26VW+99ZYiIiLUvXv3Eu3fGbge4Y4IQPBYnXyPyUuOf2yssqmTr2v+oLur2zpcob/c/LGzGdLfI6+o2IKKUKtWLYf+LNIfd3RKok2bNjp27Jh+/PHHUtdx9dVX6/vvv1dOTo7D/OTkZEVERBQIPSXh6+ur/Px8h3lffvmlbrnlFg0bNkxt27ZVo0aNil1/aGioBgwYoPnz52vBggWKi4srdW1lxfUId0MAgscKsOSpg/cJyf6u01AHnxMKsPBbR3/WpXGo+rWpK+tfbgNZvSzq37aermnkHj+yesMNN+ibb77Rf//7X/30009KSEjQ7t27S7SNHj166LrrrtNtt92mtWvX6uDBg/rss8+0atUqSdLx48fVrFmzAh2M/2zo0KGyWCwaMWKEduzYoZ9//lnz5s1TYmKi/vnPf5apjeHh4friiy90/PhxZWT88bFQ06ZNtXbtWm3ZskV79+7V/fffr7S0tGJv895779XChQu1d+9excbGlqm+suB6hLshAMGjtfBOV5Dlj5FMwZbzam4tWf8Ls3j2by3kY3UMQL5WLz3Tt7mLKiooJiZGY8eO1ZNPPqmOHTvqzJkzGjFiRIm3s3TpUnXs2FFDhgxRixYt9OSTT9rvuuTl5Wnfvn06d+5cketXr15dmzZtUl5envr376927drplVde0cyZM3X//feXun3SHx2/Dx06pMaNG6tWrVqSpGeffVYdOnRQTEyMevbsqbCwsEK/iLEo0dHRqlu3rmJiYlSvXr0y1VdWXI9wJxbjrx+qm1RWVpaCg4OVmZmpoKAgV5eDYrjUqJM/S82vqnW5TRTt+3Ox+xpUllEn58+f18GDBxURESF/f/8ybes/mw7o+T99J8uzfZvr3u7lN0IKFePs2bOqX7++5s+fr1tvvbXI5cp6LnE9wlVK+/ebO0DweGHWs7rTP4WOlpcR2zVcjWr90ZG2Ua1AxXYNd21BKBObzab09HRNnDhR1atXV//+/V1dkiSuR7gPAhBMoahRTvgfH6uXXhjYWtX8vTV5YGv5WHl5qMyOHDmiOnXqaPHixZo3b568vd3na9+4HuEO3OeKAOBy1zQK1bdje8ub8FPphYeHF/jaAAD/w6scAAeEHwBmwCsdAAAwHQIQAAAwHQIQAAAwHQIQAAAwHQIQAAAwHQIQAAAwHb4HCPBQxf1pAmcozU8V3HXXXVq4cGGB+TExMfYfJy1Pzz33nD788MMS/6I8AM/gtneAZs2apfDwcPn7+6tz586X/HXmBQsWyGKxOExl/V0kAOWvT58++uWXXxymd955x9VlATABtwxAS5YsUXx8vBISEpScnKy2bdsqJiZG6elF/3JwUFCQw4vo4cOHK7BiAKXh5+ensLAwh6lGjRrasGGDfH19tWnTJvuy06ZNU+3atZWWliZJWrVqla699lpVr15doaGh+tvf/qb9+/c7bP/YsWMaMmSIQkJCFBgYqKioKG3btk0LFizQ+PHjtXPnTvubpgULFlRk0wG4mFt+BDZz5kyNHDlScXFxkqTZs2frk08+0bx58/Svf/2r0HUsFovCwsIqskwA5aRnz54aPXq0hg8frp07d+rAgQMaO3as3n//fdWpU0eSlJ2drfj4eLVp00Znz57VuHHjNHDgQKWkpMjLy0tnz55Vjx49VL9+fX300UcKCwtTcnKybDabBg8erN27d2vVqlVat26dJCk4ONiVTQZQwdwuAOXm5mrHjh0aM2aMfZ6Xl5eio6O1devWItc7e/asGjZsKJvNpg4dOuiFF15Qy5Yti1w+JydHOTk59sdZWVnOaQCAYlu5cqWqVq3qMO/pp5/W008/reeff15r167Vfffdp927dys2NtbhF81vu+02h/XmzZunWrVqac+ePWrVqpUWL16skydP6uuvv1ZISIgkqUmTJvblq1atKm9vb944ASbldh+BZWRkKD8/3/4u76I6deooNTW10HWuvvpqzZs3TytWrNBbb70lm82mrl276tixY0XuZ/LkyQoODrZPDRo0cGo7AFze9ddfr5SUFIfpgQcekCT5+vrq7bff1tKlS3X+/Hm99NJLDuv+9NNPGjJkiBo1aqSgoCCFh4dL+uNX0CUpJSVF7du3t4cfAPgzt7sDVBpdunRRly5d7I+7du2q5s2b64033tDEiRMLXWfMmDGKj4+3P87KyiIEARUsMDDQ4a7MX23ZskWS9Ouvv+rXX39VYGCg/bl+/fqpYcOGmjt3rurVqyebzaZWrVopNzdXklSlSpXyLR5ApeZ2d4Bq1qwpq9Vq7+h4UVpaWrFvVfv4+Kh9+/b6+eefi1zGz89PQUFBDhMA97F//3499thjmjt3rjp37qzY2FjZbDZJ0qlTp7Rv3z49++yz6tWrl5o3b67ffvvNYf02bdooJSVFv/76a6Hb9/X1VX5+frm3A4B7crsA5Ovrq8jISCUlJdnn2Ww2JSUlOdzluZT8/Hx99913qlu3bnmVCcAJcnJylJqa6jBd/Bh82LBhiomJUVxcnObPn69du3bpxRdflCTVqFFDoaGhmjNnjn7++Wd9/vnnDnd0JWnIkCEKCwvTgAED9OWXX+rAgQNaunSpvS9heHi4Dh48qJSUFGVkZDj0CQTg+dwuAElSfHy85s6dq4ULF2rv3r168MEHlZ2dbR8VNmLECIdO0hMmTNCaNWt04MABJScna9iwYTp8+LDuvfdeVzUBQDGsWrVKdevWdZiuvfZaTZo0SYcPH9Ybb7whSapbt67mzJmjZ599Vjt37pSXl5feffdd7dixQ61atdJjjz2m6dOnO2zb19dXa9asUe3atXXzzTerdevWmjJliqxWq6Q/OlH36dNH119/vWrVqsX3DwEm45Z9gAYPHqyTJ09q3LhxSk1NVbt27bRq1Sp7x+gjR47Iy+t/2e23337TyJEjlZqaqho1aigyMlJbtmxRixYtXNUEwOVK8+3MFWnBggWX/O6dcePGOTy+9dZbHe7SREdHa8+ePQ7LGIbh8Lhhw4b64IMPCt2+n59fkc8B8HxuGYAkadSoURo1alShz23YsMHh8UsvvVRghAgAAEBR3PIjMAAAgPJEAAIAAKZDAAIAAKZDAAI8wF87/wIlxTkEsyEAAZWYj4+PJOncuXMurgSV3cVz6OI5BXg6tx0FBuDyrFarqlevrvT0dElSQECALBaLi6tCZWIYhs6dO6f09HRVr17d/j1JgKcjAAGV3MWfiLkYgoDSqF69erF/bgjwBAQgoJKzWCyqW7euateurby8PFeXg0rIx8eHOz8wHQIQ4CGsVit/xACgmOgEDQAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATIcABAAATMdtA9CsWbMUHh4uf39/de7cWdu3by/Weu+++64sFosGDBhQvgUCAIBKyy0D0JIlSxQfH6+EhAQlJyerbdu2iomJUXp6+iXXO3TokB5//HF17969gioFAACVkVsGoJkzZ2rkyJGKi4tTixYtNHv2bAUEBGjevHlFrpOfn6+hQ4dq/PjxatSoUQVWCwAAKhu3C0C5ubnasWOHoqOj7fO8vLwUHR2trVu3FrnehAkTVLt2bd1zzz3F2k9OTo6ysrIcJgAAYA5uF4AyMjKUn5+vOnXqOMyvU6eOUlNTC11n8+bNevPNNzV37txi72fy5MkKDg62Tw0aNChT3QAAoPJwuwBUUmfOnNHw4cM1d+5c1axZs9jrjRkzRpmZmfbp6NGj5VglAABwJ96uLuCvatasKavVqrS0NIf5aWlpCgsLK7D8/v37dejQIfXr188+z2azSZK8vb21b98+NW7cuMB6fn5+8vPzc3L1AACgMnC7O0C+vr6KjIxUUlKSfZ7NZlNSUpK6dOlSYPlmzZrpu+++U0pKin3q37+/rr/+eqWkpPDRFgAAKMDt7gBJUnx8vGJjYxUVFaVOnTopMTFR2dnZiouLkySNGDFC9evX1+TJk+Xv769WrVo5rF+9enVJKjAfAABActMANHjwYJ08eVLjxo1Tamqq2rVrp1WrVtk7Rh85ckReXm538woAAFQSbhmAJGnUqFEaNWpUoc9t2LDhkusuWLDA+QUBAACPwW0UAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOgQgAABgOm4bgGbNmqXw8HD5+/urc+fO2r59e5HLLlu2TFFRUapevboCAwPVrl07LVq0qAKrBQAAlYlbBqAlS5YoPj5eCQkJSk5OVtu2bRUTE6P09PRClw8JCdEzzzyjrVu3ateuXYqLi1NcXJxWr15dwZUDAIDKwC0D0MyZMzVy5EjFxcWpRYsWmj17tgICAjRv3rxCl+/Zs6cGDhyo5s2bq3Hjxnr00UfVpk0bbd68uYIrBwAAlYHbBaDc3Fzt2LFD0dHR9nleXl6Kjo7W1q1bL7u+YRhKSkrSvn37dN111xW5XE5OjrKyshwmAABgDm4XgDIyMpSfn686deo4zK9Tp45SU1OLXC8zM1NVq1aVr6+v+vbtq1dffVW9e/cucvnJkycrODjYPjVo0MBpbQAAAO7N7QJQaVWrVk0pKSn6+uuvNWnSJMXHx2vDhg1FLj9mzBhlZmbap6NHj1ZcsQAAwKW8XV3AX9WsWVNWq1VpaWkO89PS0hQWFlbkel5eXmrSpIkkqV27dtq7d68mT56snj17Frq8n5+f/Pz8nFY3AACoPMp8B+jXX3+VzWZzRi2SJF9fX0VGRiopKck+z2azKSkpSV26dCn2dmw2m3JycpxWFwAA8BylugO0Z88effTRR/roo4+0bds21ahRQzfffLNuueUW9enTR4GBgWUqKj4+XrGxsYqKilKnTp2UmJio7OxsxcXFSZJGjBih+vXra/LkyZL+6M8TFRWlxo0bKycnR59++qkWLVqk119/vUx1AAAAz1TsALRv3z7NmTNHH330kdLS0tS7d2898MAD+uijj3TgwAF9/PHHmjBhgoYNG6aePXuqf//+evDBB0tV1ODBg3Xy5EmNGzdOqampateunVatWmXvGH3kyBF5ef3v5lV2drb+8Y9/6NixY6pSpYqaNWumt956S4MHDy7V/gEAgGezGIZhFGfB+fPna9u2bbrlllvUq1cv+fr6FrrcoUOHtGLFCq1cuVJr1651arHlKSsrS8HBwcrMzFRQUJCry0ExjB8/vty2nZCQUG7bBjwR1yNcpbR/v4t9B+jitytfTnh4uB599FE9+uijxS4CAACgIpWpE/TFPjjJycl0OAYAAJVGmYbBXxxiPmXKFH3//ffy8vJSy5Yt1aZNG7Vp00YdO3Ys8IWGAAAArlamAHRxWPp7770nSfr999+1e/du7dq1S2vXrlVCQoJuvvlmTZw4seyVAgAAOEmJAlD9+vUVGRmpyMhIdejQQR06dFD9+vXtz1epUkUdO3ZUx44d7fMiIyMJQAAAwK2UKAD961//UnJyspYtW6ZJkyYpPz9ftWrVUocOHRxCUcOGDe3rfPXVV04vGgAAoCxKFIAefvhh+//n5OQoJSVFycnJSk5O1qeffqoZM2YoLy9PFy5csC/n4+PjvGoBAACcoNR9gPz8/NS5c2d16NBBq1evVl5eng4ePFjk9wMBAAC4i1INgz9//ryWL1+uoUOHqlatWoqLi5PVatWiRYt08uRJZ9cIAADgVCW6A7RkyRItXbpUn332mapVq6aBAwdq6dKl6tmzp6xWa3nVCAAA4FQlCkBDhgxRvXr1NH36dN17773y9i7TKHoAAACXKNFHYN27d9eZM2f0j3/8Q8HBwerSpYseeughzZs3TykpKQ6dnwEAANxViW7hbNy4UZL0008/aceOHfYRYO+8845Onz4tPz8/tW7dWtu3by+XYgEAAJyhVJ9hNW3aVE2bNtUdd9xhn3fw4EF98803+vbbb51WHAAAQHkodgBKTU1VjRo15OfnV+jzERERioiI0KBBgyRJBw4cUKNGjZxTJQAAgBMVuw/QBx98oJCQEA0cOFDz588vdLj7tm3b9PTTT6tly5Zq27atUwsFAABwlmIHoFGjRmnnzp3q3r27FixYoCuuuELXXnutXnjhBY0cOVJ169bVgAEDlJ6erilTpvB9QAAAwG2VqA9QkyZNFB8fr/j4eJ06dUorV67Up59+qvDwcC1dulRdunSRxWIpr1oBAACcotRf5BMaGqrY2FjFxsY6sx4AAIByV6qfwgAAAKjMCEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEBwiQv5NleXUO7M0EZ4BjOcq2ZoI0qGAIQK99WBU2o/ca22HTjl6lLKjRnaCM9ghnPVDG1EyRGAUKHy8m0as+w7nTl/QWOWf6c8D3xXZoY2wjOY4Vw1QxtROgQgVKiFWw7pYEa2JOnAyWwt3HLItQWVAzO0EZ7BDOeqGdqI0iEAocKkZZ3XjDX7HOa9uOZHpWWdd1FFzmeGNsIzmOFcNUMbUXoEIFSY51fuUV6+4TAvN9+mSZ/sdVFFzmeGNsIzmOFcNUMbUXoEIFSILfsz9PGuX5Rvc3wxyrcZ+mjnCW3dX/k7J5qhjfAMZjhXzdBGlI23qwuAZxg/fvwln9+UGy4pVJKlkGcNjZ23Ut19DxW6bkJCQhmrcw4ztBGe41Lnq6ecq2ZoI8oPd4BQIZpYT6nwFyJJsqipNaMiyykXZmgjPIMZzlUztBFlQwBChahrPaMIr1OyyPF2tEWGIrxOKcx61kWVOY8Z2gjPYIZz1QxtRNkQgFBhOvkek5ccv4PDKps6+R5zUUXOZ4Y2wjOY4Vw1QxtRegQgVJgAS546eJ+Q7O/IDHXwOaEAS54ry3IqM7QRnsEM56oZ2ojSIwChQrXwTleQ5Y/v4Ai2nFdza7qLK3I+M7QRnsEM56oZ2ojSIQChQnlZDHXzOSwfXVBXn8PyshiXX6mSMUMb4RnMcK6aoY0oHYbBo8KFWc/qTv8UeRU1QMMDmKGN8AxmOFfN0EaUHHeA4BJmeCEyQxvhGcxwrpqhjSgZAhAAADAdAhAAADAdAhAAADAdAhAAADAdtw1As2bNUnh4uPz9/dW5c2dt3769yGXnzp2r7t27q0aNGqpRo4aio6MvuTwAADA3twxAS5YsUXx8vBISEpScnKy2bdsqJiZG6emFf4HVhg0bNGTIEK1fv15bt25VgwYNdOONN+r48eMVXDkAAKgM3DIAzZw5UyNHjlRcXJxatGih2bNnKyAgQPPmzSt0+bffflv/+Mc/1K5dOzVr1kz/+c9/ZLPZlJSUVMGVAwCAysDtAlBubq527Nih6Oho+zwvLy9FR0dr69atxdrGuXPnlJeXp5CQkCKXycnJUVZWlsMEAADMwe0CUEZGhvLz81WnTh2H+XXq1FFqamqxtvHUU0+pXr16DiHqryZPnqzg4GD71KBBgzLVDQAAKg+3C0BlNWXKFL377rtavny5/P39i1xuzJgxyszMtE9Hjx6twCoBAIArud1vgdWsWVNWq1VpaWkO89PS0hQWFnbJdWfMmKEpU6Zo3bp1atOmzSWX9fPzk5+fX5nrBQAAlY/b3QHy9fVVZGSkQwfmix2au3TpUuR606ZN08SJE7Vq1SpFRUVVRKkAAKCScrs7QJIUHx+v2NhYRUVFqVOnTkpMTFR2drbi4uIkSSNGjFD9+vU1efJkSdLUqVM1btw4LV68WOHh4fa+QlWrVlXVqlVd1g4AAOCe3DIADR48WCdPntS4ceOUmpqqdu3aadWqVfaO0UeOHJGX1/9uXr3++uvKzc3V3//+d4ftJCQk6LnnnqvI0gEAQCXglgFIkkaNGqVRo0YV+tyGDRscHh86dKj8CwIAAB7D7foAAQAAlDcCEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB23DUCzZs1SeHi4/P391blzZ23fvr3IZb///nvddtttCg8Pl8ViUWJiYsUVCgAAKh23DEBLlixRfHy8EhISlJycrLZt2yomJkbp6emFLn/u3Dk1atRIU6ZMUVhYWAVXCwAAKhu3DEAzZ87UyJEjFRcXpxYtWmj27NkKCAjQvHnzCl2+Y8eOmj59uu644w75+flVcLUAAKCycbsAlJubqx07dig6Oto+z8vLS9HR0dq6davT9pOTk6OsrCyHCQAAmIPbBaCMjAzl5+erTp06DvPr1Kmj1NRUp+1n8uTJCg4Otk8NGjRw2rYBAIB7c7sAVFHGjBmjzMxM+3T06FFXlwQAACqIt6sL+KuaNWvKarUqLS3NYX5aWppTOzj7+fnRXwgAAJNyuztAvr6+ioyMVFJSkn2ezWZTUlKSunTp4sLKAACAp3C7O0CSFB8fr9jYWEVFRalTp05KTExUdna24uLiJEkjRoxQ/fr1NXnyZEl/dJzes2eP/f+PHz+ulJQUVa1aVU2aNHFZOwAAgHtyywA0ePBgnTx5UuPGjVNqaqratWunVatW2TtGHzlyRF5e/7t5deLECbVv397+eMaMGZoxY4Z69OihDRs2VHT5AADAzbllAJKkUaNGadSoUYU+99dQEx4eLsMwKqAqAADgCdyuDxAAAEB5IwABAADTIQABAADTIQABAADTIQABAADTIQABAADTIQABAADTIQABAADTIQABAADTIQABAADTIQABAADTIQABAADTIQABAADTIQABAADTIQABAADTIQABAADTIQABAADTIQABAADTIQABAADTIQABAADTIQABAADTIQABAADTIQABAADTIQABAADTIQABAADTIQABAADTIQABAADTIQABAADTIQABAADTIQABAADTIQABAADTIQBBF/Jtri4BTsBx9AwcR8/BsXRvBCCT++rAKbWfuFbbDpxydSkoA46jZ+A4eg6OpfsjAJlYXr5NY5Z9pzPnL2jM8u+Ux7uVSonj6Bk4jp6DY1k5EIBMbOGWQzqYkS1JOnAyWwu3HHJtQSgVjqNn4Dh6Do5l5UAAMqm0rPOasWafw7wX1/yotKzzLqoIpcFx9AwcR8/Bsaw8CEAm9fzKPcrLNxzm5ebbNOmTvS6qCKXBcfQMHEfPwbGsPAhAJrRlf4Y+3vWL8m2OF2m+zdBHO09o63467VUGHEfPwHH0HBzLysXb1QWgoAv5Nnlby5ZNx48fX+Rzm3LDJYVKshTyrKGx81aqu++hQtdNSEgoU10omfI6jpJzjqUzzlV33p+z9unuxxHFc6njKLn+tbWyXh+uUjmr9mAVMXSyifWUCr9AJcmiptaMcts3nMfVx7Gih/m6Ylgx1yNKwpXH0lOvj/JEAHIjFTV0sq71jCK8Tskix9u0FhmK8DqlMOvZctkvnMuVx7Gih/m6Ylgx1yNKylXH0pOvj/JEAHIjFTl0spPvMXnJ8YS1yqZOvsfKbZ9wPlcdx4oe5uuKYcVcjygNVxxLT78+ygsByE1U9NDJAEueOnifkOzvVAx18DmhAEteuewP5cMVx7Giz1VXDCvmekRpVfSxNMP1UV4IQG7CFUMnW3inK8jyxwkbbDmv5tb0ctsXyk9FH8eKPlddcW1wPaIsKvJYmuX6KA8EIDfgqqGTXhZD3XwOy0cX1NXnsLwsxuVXgtupyONY0eeqK64NrkeUVUUdSzNdH+WBYfAVwJ2HToZZz+pO/xR5FTVwAZWCs46jK87Vih4izvWIilAR12RFX4/ltU9X4Q6QG3D1MFhebD1DRRzHij5XXXFtcD3CWcr7WJrx+nAmApAbYBgsKouKPlddcW1wPaKy4PooGwKQm2AYLCqLij5XXXFtcD2isuD6KD0CkJtgGCwqi4o+V11xbXA9orLg+ig9ApAbYRgsKouKPlddcW1wPaKy4PooHQKQG2EYLCqLij5XXXFtcD2isuD6KB2GwbsZhsGisqjoc9UV1wbXIyoLro+S4w6QG6qsJxPMp6LPVVdcG1yPqCy4PkrGbQPQrFmzFB4eLn9/f3Xu3Fnbt2+/5PLvv/++mjVrJn9/f7Vu3VqffvppBVUKAAAqG7cMQEuWLFF8fLwSEhKUnJystm3bKiYmRunphXey2rJli4YMGaJ77rlH3377rQYMGKABAwZo9+7dFVw5AACoDNwyAM2cOVMjR45UXFycWrRoodmzZysgIEDz5s0rdPmXX35Zffr00RNPPKHmzZtr4sSJ6tChg1577bUKrhwAAFQGbheAcnNztWPHDkVHR9vneXl5KTo6Wlu3bi10na1btzosL0kxMTFFLg8AAMzN7UaBZWRkKD8/X3Xq1HGYX6dOHf3www+FrpOamlro8qmpqUXuJycnRzk5OfbHmZmZkqSsrKzSll6k8+fPO32bFxVVb3nts6L35077pI3O358r9mmGNpbnPmlj+TBzG521XcMo4VB8w80cP37ckGRs2bLFYf4TTzxhdOrUqdB1fHx8jMWLFzvMmzVrllG7du0i95OQkGDoj6+xZGJiYmJiYqrk09GjR0uUN9zuDlDNmjVltVqVlpbmMD8tLU1hYWGFrhMWFlai5SVpzJgxio+Ptz+22Wz69ddfFRoaKovFdeP6srKy1KBBAx09elRBQUEuq6M80UbPQBs9A230DGZuo2EYOnPmjOrVq1ei7bldAPL19VVkZKSSkpI0YMAASX+Ek6SkJI0aNarQdbp06aKkpCSNHj3aPm/t2rXq0qVLkfvx8/OTn5+fw7zq1auXtXynCQoK8tiT+CLa6Bloo2egjZ7BrG0MDg4u8XbcLgBJUnx8vGJjYxUVFaVOnTopMTFR2dnZiouLkySNGDFC9evX1+TJkyVJjz76qHr06KEXX3xRffv21bvvvqtvvvlGc+bMcWUzAACAm3LLADR48GCdPHlS48aNU2pqqtq1a6dVq1bZOzofOXJEXl7/G8DWtWtXLV68WM8++6yefvppNW3aVB9++KFatWrlqiYAAAA35pYBSJJGjRpV5EdeGzZsKDBv0KBBGjRoUDlXVf78/PyUkJBQ4OM5T0IbPQNt9Ay00TPQxpKzGEZJx40BAABUbm73RYgAAADljQAEAABMhwAEAABMhwAEAABMhwDkRmbNmqXw8HD5+/urc+fO2r59u6tLcprJkyerY8eOqlatmmrXrq0BAwZo3759ri6rXE2ZMkUWi8XhCzo9wfHjxzVs2DCFhoaqSpUqat26tb755htXl+U0+fn5Gjt2rCIiIlSlShU1btxYEydOLPnvDLmZL774Qv369VO9evVksVj04YcfOjxvGIbGjRununXrqkqVKoqOjtZPP/3kmmJL6VJtzMvL01NPPaXWrVsrMDBQ9erV04gRI3TixAnXFVwKlzuOf/bAAw/IYrEoMTGxwupzhuK0ce/everfv7+Cg4MVGBiojh076siRIyXaDwHITSxZskTx8fFKSEhQcnKy2rZtq5iYGKWnp7u6NKfYuHGjHnroIX311Vdau3at8vLydOONNyo7O9vVpZWLr7/+Wm+88YbatGnj6lKc6rffflO3bt3k4+Ojzz77THv27NGLL76oGjVquLo0p5k6dapef/11vfbaa9q7d6+mTp2qadOm6dVXX3V1aWWSnZ2ttm3batasWYU+P23aNL3yyiuaPXu2tm3bpsDAQMXExJTrj2M626XaeO7cOSUnJ2vs2LFKTk7WsmXLtG/fPvXv398FlZbe5Y7jRcuXL9dXX31V4p+HcAeXa+P+/ft17bXXqlmzZtqwYYN27dqlsWPHyt/fv2Q7KtEvh6HcdOrUyXjooYfsj/Pz84169eoZkydPdmFV5Sc9Pd2QZGzcuNHVpTjdmTNnjKZNmxpr1641evToYTz66KOuLslpnnrqKePaa691dRnlqm/fvsbdd9/tMO/WW281hg4d6qKKnE+SsXz5cvtjm81mhIWFGdOnT7fPO336tOHn52e88847Lqiw7P7axsJs377dkGQcPny4YopysqLaeOzYMaN+/frG7t27jYYNGxovvfRShdfmLIW1cfDgwcawYcPKvG3uALmB3Nxc7dixQ9HR0fZ5Xl5eio6O1tatW11YWfnJzMyUJIWEhLi4Eud76KGH1LdvX4fj6Sk++ugjRUVFadCgQapdu7bat2+vuXPnurosp+ratauSkpL0448/SpJ27typzZs366abbnJxZeXn4MGDSk1NdThng4OD1blzZ499DZL+eB2yWCxu9TuQZWWz2TR8+HA98cQTatmypavLcTqbzaZPPvlEV111lWJiYlS7dm117tz5kh8FFoUA5AYyMjKUn59v/6mPi+rUqaPU1FQXVVV+bDabRo8erW7dunncz5W8++67Sk5Otv9Onac5cOCAXn/9dTVt2lSrV6/Wgw8+qEceeUQLFy50dWlO869//Ut33HGHmjVrJh8fH7Vv316jR4/W0KFDXV1aubn4OmOW1yBJOn/+vJ566ikNGTLEo348dOrUqfL29tYjjzzi6lLKRXp6us6ePaspU6aoT58+WrNmjQYOHKhbb71VGzduLNG23PanMOC5HnroIe3evVubN292dSlOdfToUT366KNau3ZtyT+LriRsNpuioqL0wgsvSJLat2+v3bt3a/bs2YqNjXVxdc7x3nvv6e2339bixYvVsmVLpaSkaPTo0apXr57HtNHs8vLydPvtt8swDL3++uuuLsdpduzYoZdfflnJycmyWCyuLqdc2Gw2SdItt9yixx57TJLUrl07bdmyRbNnz1aPHj2KvS3uALmBmjVrymq1Ki0tzWF+WlqawsLCXFRV+Rg1apRWrlyp9evX64orrnB1OU61Y8cOpaenq0OHDvL29pa3t7c2btyoV155Rd7e3srPz3d1iWVWt25dtWjRwmFe8+bNSzz6wp098cQT9rtArVu31vDhw/XYY4957F09SfbXGTO8Bl0MP4cPH9batWs96u7Ppk2blJ6eriuvvNL+GnT48GH985//VHh4uKvLc4qaNWvK29vbKa9DBCA34Ovrq8jISCUlJdnn2Ww2JSUlqUuXLi6szHkMw9CoUaO0fPlyff7554qIiHB1SU7Xq1cvfffdd0pJSbFPUVFRGjp0qFJSUmS1Wl1dYpl169atwNcX/Pjjj2rYsKGLKnK+c+fOycvL8aXRarXa33l6ooiICIWFhTm8BmVlZWnbtm0e8xok/S/8/PTTT1q3bp1CQ0NdXZJTDR8+XLt27XJ4DapXr56eeOIJrV692tXlOYWvr686duzolNchPgJzE/Hx8YqNjVVUVJQ6deqkxMREZWdnKy4uztWlOcVDDz2kxYsXa8WKFapWrZq9X0FwcLCqVKni4uqco1q1agX6NAUGBio0NNRj+jo99thj6tq1q1544QXdfvvt2r59u+bMmaM5c+a4ujSn6devnyZNmqQrr7xSLVu21LfffquZM2fq7rvvdnVpZXL27Fn9/PPP9scHDx5USkqKQkJCdOWVV2r06NF6/vnn1bRpU0VERGjs2LGqV6+eBgwY4LqiS+hSbaxbt67+/ve/Kzk5WStXrlR+fr79dSgkJES+vr6uKrtELncc/xrqfHx8FBYWpquvvrqiSy21y7XxiSee0ODBg3Xdddfp+uuv16pVq/Txxx9rw4YNJdtRmceRwWleffVV48orrzR8fX2NTp06GV999ZWrS3IaSYVO8+fPd3Vp5crThsEbhmF8/PHHRqtWrQw/Pz+jWbNmxpw5c1xdklNlZWUZjz76qHHllVca/v7+RqNGjYxnnnnGyMnJcXVpZbJ+/fpCr8HY2FjDMP4YCj927FijTp06hp+fn9GrVy9j3759ri26hC7VxoMHDxb5OrR+/XpXl15slzuOf1UZh8EXp41vvvmm0aRJE8Pf399o27at8eGHH5Z4PxbDqORfbwoAAFBC9AECAACmQwACAACmQwACAACmQwACAACmQwACAACmQwACAACmQwACAACmQwACAACmQwACAACmQwACUOn17NlTo0ePLpdtP/HEE+rXr1+5bBuA6/BTGAAqvV9//VU+Pj6qVq2apD8CUbt27ZSYmFjmbZ8+fVpWq9W+bQCegV+DB1DphYSElNu2q1evXm7bBuA6fAQGoFL44IMP1Lp1a1WpUkWhoaGKjo5Wdna2JMePwO666y5t3LhRL7/8siwWiywWiw4dOiSbzabJkycrIiJCVapUUdu2bfXBBx9ccp8ZGRmyWCzavXt3eTcPQAXjDhAAt/fLL79oyJAhmjZtmgYOHKgzZ85o06ZNKuwT/Jdfflk//vijWrVqpQkTJkiSatWqpcmTJ+utt97S7Nmz1bRpU33xxRcaNmyYatWqpR49ehS63507d8rPz0/NmjUr1/YBqHgEIABu75dfftGFCxd06623qmHDhpKk1q1bF7pscHCwfH19FRAQoLCwMElSTk6OXnjhBa1bt05dunSRJDVq1EibN2/WG2+8cckA1LJlS3l781IJeBquagBur23bturVq5dat26tmJgY3Xjjjfr73/+uGjVqFGv9n3/+WefOnVPv3r0d5ufm5qp9+/ZFrpeSkqJ27dqVpXQAbooABMDtWa1WrV27Vlu2bNGaNWv06quv6plnntG2bdsUERFx2fXPnj0rSfrkk09Uv359h+f8/PyKXG/nzp265557ylY8ALdEJ2gAlYLFYlG3bt00fvx4ffvtt/L19dXy5csLXdbX11f5+fn2xy1atJCfn5+OHDmiJk2aOEwNGjQodBu5ubnau3ev2rZtWy7tAeBa3AEC4Pa2bdumpKQk3Xjjjapdu7a2bdumkydPqnnz5oUuHx4erm3btunQoUOqWrWqQkJC9Pjjj+uxxx6TzWbTtddeq8zMTH355ZcKCgpSbGxsgW3s3btXeXl5BCDAQxGAALi9oKAgffHFF0pMTFRWVpYaNmyoF198UTfddFOhyz/++OOKjY1VixYt9Pvvv+vgwYOaOHGifTTYgQMHVL16dXXo0EFPP/10odtISUlRw4YN+R4gwEPxTdAAUIhRo0YpPT1d7733nqtLAVAO6AMEAH9y/vx57dixQ0uXLlVMTIyrywFQTghAAPAniYmJio6O1i233KIRI0a4uhwA5YSPwAAAgOlwBwgAAJgOAQgAAJgOAQgAAJgOAQgAAJgOAQgAAJgOAQgAAJgOAQgAAJgOAQgAAJgOAQgAAJgOAQgAAJgOAQgAAJjO/wGbkesAzCQrgAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.bar(range(N_s), exact_data[0], color='grey', label='Exact')\n",
    "plt.scatter(range(N_s), trunc_data[0], marker='d', label='Trunc. Unitary')\n",
    "plt.xlabel(r'site $j$')\n",
    "plt.ylabel(r'$\\langle N_j \\rangle$')\n",
    "plt.legend()\n",
    "title = \"(a) MPS Initial State \"\n",
    "plt.title(title)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 571,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(1.6817304007466387)"
      ]
     },
     "execution_count": 571,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "occs_perc_errs = []\n",
    "for i in range(N_t-1):\n",
    "    for j in range(N_s):\n",
    "        if exact_data[i][j] > 1E-5:\n",
    "            diff = np.abs(truncu_data[i][j] - exact_data[i][j])\n",
    "            perc_err = diff / exact_data[i][j] * 100\n",
    "            occs_perc_errs.append(perc_err)\n",
    "# occs_perc_errs = np.array(occs_perc_errs).reshape((120, 16))\n",
    "np.mean(occs_perc_errs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 531,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(0.0014133416343790472)"
      ]
     },
     "execution_count": 531,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(occs_perc_errs[2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 580,
   "metadata": {},
   "outputs": [],
   "source": [
    "exact_EEs = np.loadtxt(\"Data/ising-exact-EEs-N_s16-J0.4-h1-g0.01-width1.5-dt0.1.txt\", dtype='float')\n",
    "trunc_EEs = np.loadtxt(\"Data/ising-approx-EEs-N_s16-J0.4-h1-g0.01-width1.5-dt0.1.txt\", dtype='float')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 581,
   "metadata": {},
   "outputs": [],
   "source": [
    "region = np.linspace(0, N_s-2, N_s-2)\n",
    "times = np.linspace(0, N_t * dt, N_t)\n",
    "Region, Times = np.meshgrid(region, times)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 582,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.        ,  1.07692308,  2.15384615,  3.23076923,  4.30769231,\n",
       "        5.38461538,  6.46153846,  7.53846154,  8.61538462,  9.69230769,\n",
       "       10.76923077, 11.84615385, 12.92307692, 14.        ])"
      ]
     },
     "execution_count": 582,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "region"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 583,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.        ,  1.07692308,  2.15384615,  3.23076923,  4.30769231,\n",
       "        5.38461538,  6.46153846,  7.53846154,  8.61538462,  9.69230769,\n",
       "       10.76923077, 11.84615385, 12.92307692, 14.        ])"
      ]
     },
     "execution_count": 583,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "region"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 584,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7c5d4493bd90>"
      ]
     },
     "execution_count": 584,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.pcolormesh(Region[1:,:], Times[1:,:], exact_EEs[1:,:], cmap='inferno')\n",
    "plt.xlabel(r'Region $R=(0, j+1)$')\n",
    "plt.ylabel(r't')\n",
    "title = r'$S_R (t)$: $N_s = $' + str(N_s)\n",
    "title += r', $J = $' + str(J)\n",
    "title += r', $h = $' + str(h)\n",
    "title += r', $g = $' + str(g)\n",
    "title += r', $\\Delta t=$' + str(dt)\n",
    "plt.title(title)\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 586,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7c5d448eb390>"
      ]
     },
     "execution_count": 586,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.pcolormesh(Region[1:,:], Times[1:,:], trunc_EEs[1:,:], cmap='inferno')\n",
    "plt.xlabel(r'Region $R=(0, j+1)$')\n",
    "plt.ylabel(r't')\n",
    "title = r'(b) $S_R (t)$: $N_s = $' + str(N_s)\n",
    "title += r', $J = $' + str(J)\n",
    "title += r', $h = $' + str(h)\n",
    "title += r', $g = $' + str(g)\n",
    "# title += r', $\\Delta t=$' + str(dt)\n",
    "plt.title(title)\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 366,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(121, 14)"
      ]
     },
     "execution_count": 366,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trunc_EEs.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 367,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7c5d4810f110>"
      ]
     },
     "execution_count": 367,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.bar(range(N_s-2), exact_EEs[1,:], color='grey')\n",
    "plt.scatter(range(N_s-2), trunc_EEs[1,:], marker='d')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 368,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7c5d481c1090>"
      ]
     },
     "execution_count": 368,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "diff = np.abs(exact_EEs[1:,:] - trunc_EEs[1:,:]) / exact_EEs[1:,:]*100\n",
    "plt.pcolormesh(Region[1:,:], Times[1:,:], diff, cmap='inferno')\n",
    "plt.xlabel(r'Region $R=(0, j+1)$')\n",
    "plt.ylabel(r't')\n",
    "title = r'Abs. Diff. $S_r (t)$: $N_s = $' + str(N_s)\n",
    "title += r', $J = $' + str(J)\n",
    "title += r', $h = $' + str(h)\n",
    "title += r', $g = $' + str(g)\n",
    "# title += r', $\\Delta t=$' + str(dt)\n",
    "plt.title(title)\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 369,
   "metadata": {},
   "outputs": [],
   "source": [
    "S_perc_errs = []\n",
    "for i in range(1,N_t):\n",
    "        for j in range(N_s-2):\n",
    "                if exact_EEs[i,j] > 1E-6:\n",
    "                        diff = np.abs(exact_EEs[i,j] - trunc_EEs[i,j])\n",
    "                        perc_err = diff / exact_EEs[i] * 100\n",
    "                        S_perc_errs.append(perc_err)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 370,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(18.481648851728075)"
      ]
     },
     "execution_count": 370,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(S_perc_errs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.13.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
